共查询到20条相似文献，搜索用时 109 毫秒
1.
Cross-borehole flowmeter tests have been proposed as an efficient method to investigate preferential flowpaths in heterogeneous aquifers, which is a major task in the characterization of fractured aquifers. Cross-borehole flowmeter tests are based on the idea that changing the pumping conditions in a given aquifer will modify the hydraulic head distribution in large-scale flowpaths, producing measurable changes in the vertical flow profiles in observation boreholes. However, inversion of flow measurements to derive flowpath geometry and connectivity and to characterize their hydraulic properties is still a subject of research. In this study, we propose a framework for cross-borehole flowmeter test interpretation that is based on a two-scale conceptual model: discrete fractures at the borehole scale and zones of interconnected fractures at the aquifer scale. We propose that the two problems may be solved independently. The first inverse problem consists of estimating the hydraulic head variations that drive the transient borehole flow observed in the cross-borehole flowmeter experiments. The second inverse problem is related to estimating the geometry and hydraulic properties of large-scale flowpaths in the region between pumping and observation wells that are compatible with the head variations deduced from the first problem. To solve the borehole-scale problem, we treat the transient flow data as a series of quasi-steady flow conditions and solve for the hydraulic head changes in individual fractures required to produce these data. The consistency of the method is verified using field experiments performed in a fractured-rock aquifer. 相似文献
2.
Alluvial fans are potential sites of potable groundwater in many parts of the world. Characteristics of alluvial fans sediments are changed radially from high energy coarse-grained deposition near the apex to low energy fine-grained deposition downstream so that patchy wedge-shaped aquifers with radial heterogeneity are formed. The hydraulic parameters of the aquifers (e.g. hydraulic conductivity and specific storage) change in the same fashion. Analytical or semi-analytical solutions of the flow in wedge-shaped aquifers are available for homogeneous cases. In this paper we derive semi-analytical solutions of groundwater flow to a well in multi-zone wedge-shaped aquifers. Solutions are provided for three wedge boundary configurations namely: constant head–constant head wedge, constant head–barrier wedge and barrier–barrier wedge. Derivation involves the use of integral transforms methods. The effect of heterogeneity ratios of zones on the response of the aquifer is examined. The results are presented in form of drawdown and drawdown derivative type curves. Heterogeneity has a significant effect on over all response of the pumped aquifer. Solutions help understanding the behavior of heterogeneous multi-zone aquifers for sustainable development of the groundwater resources in alluvial fans. 相似文献
3.
Georgios Etsias Gerard A. Hamill Jesús F. Águila Eric M. Benner Mark C. McDonnell Ashraf A. Ahmed Raymond Flynn 《水文研究》2021,35(4):e14120
Laboratory experiments and numerical simulations were utilized in this study to assess the impact of aquifer stratification on saltwater intrusion. Three homogeneous and six layered aquifers were investigated. Image processing algorithms facilitated the precise calculation of saltwater wedge toe length, width of the mixing zone, and angle of intrusion. It was concluded that the length of intrusion in stratified aquifers is predominantly a function of permeability contrast, total aquifer transmissivity and the number of heterogeneous layers, being positively correlated to all three. When a lower permeability layer overlays or underlays more permeable zones its mixing zone widens, while it becomes thinner for the higher permeability strata. The change in the width of the mixing zone (WMZ) is positively correlated to permeability contrast, while it applies to all strata irrespectively of their relative vertical position in the aquifer. Variations in the applied hydraulic head causes the transient widening of WMZ. These peak WMZ values are larger during saltwater retreat and are negatively correlated to the layer's permeability and distance from the aquifer's bottom. Moreover, steeper angles of intrusion are observed in cases where low permeability layers overlay more permeable strata, and milder ones in the inverse aquifer setups. The presence of a low permeability upper layer results in the confinement of the saltwater wedge in the lower part of the stratified aquifer. This occurs until a critical hydraulic head difference is applied to the system. This hydraulic gradient value was found to be a function of layer width and permeability contrast alike. 相似文献
4.
Using the first-order analysis, we investigate the spatial cross-correlation between hydraulic conductivity variation and specific discharge (flux) as well as its components measured in a borehole under steady-state flow conditions during cross-hole pumping tests in heterogeneous aquifers. These spatial correlation patterns are found to be quite different from that between the hydraulic conductivity variation and the hydraulic head measurement in the same borehole. This finding suggests that a specific discharge measurement carries non-redundant information about the spatial distribution of heterogeneity, even this measurement is collected from the same location where the head measurement is taken. As such, specific discharge observations should be included in the analysis of hydraulic tomography to increase the resolution of estimated aquifer heterogeneity. Using numerical experiments, we demonstrate the effectiveness of the joint interpretation of both hydraulic heads and fluxes for mapping fracture distributions in a hypothetic geologic medium. 相似文献
5.
One of the challenges in characterizing fractured-rock aquifers is determining whether the equivalent porous medium approximation is valid at the problem scale. Detailed hydrogeologic characterization completed at a small study site in a densely fractured dolomite has yielded an extensive data set that was used to evaluate the utility of the continuum and discrete-fracture approaches to aquifer characterization. There are two near-vertical sets of fractures at the site; near-horizontal bedding-plane partings constitute a third fracture set. Eighteen boreholes, including five coreholes, were drilled to a depth of approximately 10.6 m. Borehole geophysical logs revealed several laterally extensive horizontal fractures and dissolution zones. Flowmeter and short-interval packer testing identified which of these features were hydraulically important. A monitoring system, consisting of short-interval piezometers and multilevel samplers, was designed to monitor four horizontal fractures and two dissolution zones. The resulting network consisted of >70 sampling points and allowed detailed monitoring of head distributions in three dimensions. Comparison of distributions of hydraulic head and hydraulic conductivity determined by these two approaches suggests that even in a densely fractured-carbonate aquifer, a characterization approach using traditional long-interval monitoring wells is inadequate to characterize ground water movement for the purposes of regulatory monitoring or site remediation. In addition, traditional multiwell pumping tests yield an average or bulk hydraulic conductivity that is not adequate for predicting rapid ground water travel times through the fracture network, and the pumping test response does not appear to be an adequate tool for assessing whether the porous medium approximation is valid. 相似文献
6.
7.
Identifying connections in a fractured rock aquifer using ADFTs 总被引：1，自引：0，他引：1
Fractured rock aquifers are difficult to characterize because of their extremely heterogeneous nature. Developing an understanding of fracture network hydraulic properties in these aquifers is difficult and time consuming, and field testing techniques for determining the location and connectivity of fractures in these aquifers are limited. In the Clare Valley, South Australia, well interference is an important issue for a major viticultural area that uses a fractured aquifer. Five fracture sets exist in the aquifer, all dipping > 25 degrees . In this setting, we evaluate the ability of steady-state asymmetric dipole-flow tests (ADFTs) to determine the connections between a test well and a set of piezometers. The procedure involves dividing a test well into two chambers using a single packer and pumping fluid from the upper chamber to the lower chamber. By conducting a series of tests at different packer elevations, an "input" signal is generated in fracture zones connected to the test well. By monitoring the "output" response of the hydraulic dipole field at piezometers, the connectivity of the fractures between the test well and piezometers can be determined. Results indicate the test well used in this study is connected in a complex three-dimensional geometry, with drawdown occurring above and below areas of potentiometric buildup. The ADFT method demonstrates that the aquifer evaluated in this study cannot be modeled effectively on the well scale using continuum flow models. 相似文献
8.
Two large-scale (9.5 m long, 4.7 m wide, 2.6 m deep), three-dimensional artificial aquifers were constructed to investigate the influence of spatial variations in aquifer properties on contaminant transport. One aquifer was uniformly filled with coarse sand media (0.6 to 2.0 mm) and the other was constructed as a heterogeneous aquifer using blocks of fine, medium, and coarse sands. The key features of these artificial aquifers are described. An innovative deaeration tower was constructed to overcome a problem of the aquifers becoming blocked with excess air from the ground water source. A series of tracer injection experiments were conducted to test the homogeneity of the first aquifer that was purposely built as a homogeneous aquifer and to calculate values of aquifer parameters. Experimental data show that the aquifer is slightly heterogeneous, and hydraulic conductivity values are significantly higher down one side of the aquifer compared to the mean value. There was very good agreement in estimated dispersivity values between the plume area ratio methods and the curve fitting of tracer breakthrough curves. Dispersivity estimates from a full areal source injection (12.2 m2) experiment using a 1D analytical model were higher than estimates from a limited source injection (0.2 m2) experiment using a 3D model, possibly because the 1D model does not take account of the heterogeneity of hydraulic conductivity in the aquifer, thus overestimating dispersivity. Transverse and vertical dispersivity values were about five times less than the longitudinal dispersivity. There was slight sorption of Rhodamine WT onto the aquifer media. 相似文献
9.
Cross-well seismic reflection data, acquired from a carbonate aquifer at Port Mayaca test site near the eastern boundary of Lake Okeechobee in Martin County, Florida, are used to delineate flow units in the region intercepted by two wells. The interwell impedance determined by inversion from the seismic reflection data allows us to visualize the major boundaries between the hydraulic units. The hydraulic (flow) unit properties are based on the integration of well logs and the carbonate structure, which consists of isolated vuggy carbonate units and interconnected vug systems within the carbonate matrix. The vuggy and matrix porosity logs based on Formation Micro-Imager (FMI) data provide information about highly permeable conduits at well locations. The integration of the inverted impedance and well logs using geostatistics helps us to assess the resolution of the cross-well seismic method for detecting conduits and to determine whether these conduits are continuous or discontinuous between wells. A productive water zone of the aquifer outlined by the well logs was selected for analysis and interpretation. The ELAN (Elemental Log Analysis) porosity from two wells was selected as primary data and the reflection seismic-based impedance as secondary data. The direct and cross variograms along the vertical wells capture nested structures associated with periodic carbonate units, which correspond to connected flow units between the wells. Alternatively, the horizontal variogram of impedance (secondary data) provides scale lengths that correspond to irregular boundary shapes of flow units. The ELAN porosity image obtained by cokriging exhibits three similar flow units at different depths. These units are thin conduits developed in the first well and, at about the middle of the interwell separation region, these conduits connect to thicker flow units that are intercepted by the second well. In addition, a high impedance zone (low porosity) at a depth of about 275 m, after being converted to ELAN porosity, is characterized as a more confined low porosity structure. This continuous zone corresponds to a permeability barrier in the carbonate aquifer that separates the three connected conduits observed in the cokriging image. In the zones above and below this permeability barrier, the water production is very high, which agrees with water well observations at the Port Mayaca aquifer. 相似文献
10.
Signatures in flowing fluid electric conductivity logs 总被引：1，自引：0，他引：1
Flowing fluid electric conductivity logging provides a means to determine hydrologic properties of fractures, fracture zones, or other permeable layers intersecting a borehole in saturated rock. The method involves analyzing the time-evolution of fluid electric conductivity (FEC) logs obtained while the well is being pumped and yields information on the location, hydraulic transmissivity, and salinity of permeable layers. The original analysis method was restricted to the case in which flows from the permeable layers or fractures were directed into the borehole (inflow). Recently, the method was adapted to permit treatment of both inflow and outflow, including analysis of natural regional flow in the permeable layer. A numerical model simulates flow and transport in the wellbore during flowing FEC logging, and fracture properties are determined by optimizing the match between simulation results and observed FEC logs. This can be a laborious trial-and-error procedure, especially when both inflow and outflow points are present. Improved analyses methods are needed. One possible tactic would be to develop an automated inverse method, but this paper takes a more elementary approach and focuses on identifying the signatures that various inflow and outflow features create in flowing FEC logs. The physical insight obtained provides a basis for more efficient analysis of these logs, both for the present trial and error approach and for a potential future automated inverse approach. Inflow points produce distinctive signatures in the FEC logs themselves, enabling the determination of location, inflow rate, and ion concentration. Identifying outflow locations and flow rates typically requires a more complicated integral method, which is also presented in this paper. 相似文献
11.
This paper addresses the issue of flow in heterogeneous leaky confined aquifers subject to leakage. The leakage into the confined aquifer is driven by spatial and periodic fluctuations of water table in an overlying phreatic aquifer. The introduction of leakage leads to non-uniformity in the mean head gradient and results in nonstationarity in hydraulic head and velocity fields. Therefore, a nonstationary spectral approach based on Fourier–Stieltjes representations for the perturbed quantities is adopted to account for the spatial variability of nonstationary head fields. Closed-form expressions for the variances of hydraulic head and specific discharge are developed in terms of statistical properties of hydraulic parameters. The results indicate that the spatiotemporal variations in leakage leads to enhanced variability of the hydraulic head and of the specific discharge, which increase with distance from any arbitrary reference point. The coefficient of leakage and the spatial structure of log transmissivity field and of the amplitude of water table fluctuation are critical in quantifying the variability of the hydraulic head and of the specific discharge. 相似文献
12.
《Advances in water resources》2005,28(5):467-477
The identification of vadose zone flow parameters and solute travel time from the surface to the water table are key issues for the assessment of groundwater vulnerability. In this paper we use the results of time-lapse monitoring of the vadose zone in a UK consolidated sandstone aquifer using cross-hole zero-offset radar to assess and calibrate models of water flow in the vadose zone. The site under investigation is characterized by a layered structure, with permeable medium sandstone intercalated by finer, less permeable, laminated sandstone. Information on this structure is available from borehole geophysical (gamma-ray) logs. Monthly cross-hole radar monitoring was performed from August 1999 to February 2001, and shows small changes of moisture content over time and fairly large spatial variability with depth. One-dimensional Richards’ equation modeling of the infiltration process was performed under spatially heterogeneous, steady state conditions. Both layer structure and Richards’ equation parameters were simulated using a nested Monte Carlo approach, constrained via geostatistical analysis on the gamma-ray logs and on a priori information regarding the possible range of hydraulic parameters. The results of the Monte Carlo analysis show that, in order to match the radar-derived moisture content profiles, it is necessary to take into account the vertical scale of measurements, with an averaging window size of the order of the antenna length and the Fresnel zone width. Flow parameters cannot be uniquely identified, showing that the system is over parameterized with respect to the information content of the (nearly stationary) radar profiles. Estimates of travel time of water across the vadose zone are derived from the simulation results. 相似文献
13.
Stephen R.H. Worthington 《Ground water》2022,60(2):169-179
Flow in many bedrock aquifers is through fracture networks. Point to point tracer tests using applied tracers provide a direct measure of time of travel and are most useful for determining effective porosity. Calculated values from these tests are typically between 10−4 and 10−2 (0.01% to 1%), with these low values indicating preferential flow through fracture and channel networks. Tracer tests are not commonly used in site investigations, and specific yield is often used as a proxy for effective porosity. The most popular methods have used centrifuge measurements, water table fluctuations, pumping tests, and packer tests. Specific yield varies substantially with the testing method. No method is as reliable as tracer testing for providing estimates of effective porosity, but all methods provide complementary insights on aquifer structure. Temporal and spatial scaling effects suggest that bedrock aquifers have hierarchical structures, with a network of more permeable fractures and channels, which are connected to less permeable fractures and to the matrix. Consequences of the low effective porosities include groundwater velocities that often exceed 100 m/d and more frequent microbial contamination than in aquifers in unconsolidated sediments. The large uncertainty over the magnitude of effective porosity in bedrock aquifers makes it an important parameter to determine in studies where time of travel is of interest. 相似文献
14.
A conceptual model of anisotropic and dynamic permeability is developed from hydrogeologic and hydromechanical characterization of a foliated, complexly fractured, crystalline rock aquifer at Gates Pond, Berlin, Massachusetts. Methods of investigation include aquifer‐pumping tests, long‐term hydrologic monitoring, fracture characterization, downhole heat‐pulse flow meter measurements, in situ extensometer testing, and earth tide analysis. A static conceptual model is developed from observations of depth‐dependent and anisotropic permeability that effectively compartmentalizes the aquifer as a function of foliation intensity. Superimposed on the static model is dynamic permeability as a function of hydraulic head in which transient bulk aquifer transmissivity is proportional to changes in hydraulic head due to hydromechanical coupling. The dynamic permeability concept is built on observations that fracture aperture changes as a function of hydraulic head, as measured during in situ extensometer testing of individual fractures, and observed changes in bulk aquifer transmissivity as determined from earth tides during seasonal changes in hydraulic head, with higher transmissivity during periods of high hydraulic head, and lower transmissivity during periods of relatively lower hydraulic head. A final conceptual model is presented that captures both the static and dynamic properties of the aquifer. The workflow presented here demonstrates development of a conceptual framework for building numerical models of complexly fractured, foliated, crystalline rock aquifers that includes both a static model to describe the spatial distribution of permeability as a function of fracture type and foliation intensity and a dynamic model that describes how hydromechanical coupling impacts permeability magnitude as a function of hydraulic head fluctuation. This model captures important geologic controls on permeability magnitude, anisotropy, and transience and therefor offers potentially more reliable history matching and forecasts of different water management strategies, such as resource evaluation, well placement, permeability prediction, and evaluating remediation strategies. 相似文献
15.
Zhixue Zhao Xiaoguang Wang Yonghong Hao Tongke Wang Abderrahim Jardani Herve Jourde Tian‐Chyi Jim Yeh Ming Zhang 《水文研究》2019,33(19):2551-2560
The study on the hydraulic properties of coastal aquifers has significant implications both in hydrological sciences and environmental engineering. Although many analytical solutions are available, most of them are based on the same basic assumption that assumes aquifers extend landward semi‐infinitely, which does not necessarily reflect the reality. In this study, the general solutions for a leaky confined coastal aquifer have been developed that consider both finitely landward constant‐head and no‐flow boundaries. The newly developed solutions were then used to examine theoretically the joint effects of leakage and aquifer length on hydraulic head fluctuations within the leaky confined aquifer, and the validity of using the simplified solution, which assumes the aquifer is semi‐infinite. The results illustrated that the use of the simplified solution may cause significant errors, depending on joint effects of leakage and aquifer length. A dimensionless characteristic parameter was then proposed as an index for judging the applicability of the simplified solution. In addition, practical application of the general solution for the constant‐head inland boundary was used to characterize the hydraulic properties of a leaky confined aquifer using the data collected from a field site at the Seine River estuary, France, and the versatility of the general solution was further justified. 相似文献
16.
The Effect of Modeled Recharge Distribution on Simulated Groundwater Availability and Capture 
下载免费PDF全文
下载免费PDF全文 Simulating groundwater flow in basin‐fill aquifers of the semiarid southwestern United States commonly requires decisions about how to distribute aquifer recharge. Precipitation can recharge basin‐fill aquifers by direct infiltration and transport through faults and fractures in the high‐elevation areas, by flowing overland through high‐elevation areas to infiltrate at basin‐fill margins along mountain fronts, by flowing overland to infiltrate along ephemeral channels that often traverse basins in the area, or by some combination of these processes. The importance of accurately simulating recharge distributions is a current topic of discussion among hydrologists and water managers in the region, but no comparative study has been performed to analyze the effects of different recharge distributions on groundwater simulations. This study investigates the importance of the distribution of aquifer recharge in simulating regional groundwater flow in basin‐fill aquifers by calibrating a groundwater‐flow model to four different recharge distributions, all with the same total amount of recharge. Similarities are seen in results from steady‐state models for optimized hydraulic conductivity values, fit of simulated to observed hydraulic heads, and composite scaled sensitivities of conductivity parameter zones. Transient simulations with hypothetical storage properties and pumping rates produce similar capture rates and storage change results, but differences are noted in the rate of drawdown at some well locations owing to the differences in optimized hydraulic conductivity. Depending on whether the purpose of the groundwater model is to simulate changes in groundwater levels or changes in storage and capture, the distribution of aquifer recharge may or may not be of primary importance. 相似文献
17.
John H. Williams Wayne W. Lapham Thomas H. Barringer 《Ground Water Monitoring & Remediation》1993,13(3):129-138
Electromagnetic (EM) logging provides an efficient method for high-resolution, vertical delineation of electrically conductive contamination in glacial sand-and-gravel aquifers. LM. gamma, and lithologic logs and specific conductance data from sand-and-gravel aquifers at five sites in the northeastern United States were analyzed to define the relation of KM conductivity to aquifer lithology and water quality. Municipal waste disposal, septic waste discharge, or highway deicing salt application at these sites has caused contaminant plumes in which the dissolved solids concentration and specific conductance of ground water exceed background levels by as much as 10 to 20 limes.
The major hydrogeologic factors that affected KM log response at the five sites were the dissolved solids concentration of the ground water and the silt and clay content in the aquifer. KM conductivity of sand and gravel with uncontaminated water ranged from less than 5 to about 10 millisiemens per meter (mS/m); that of silt and clay zones ranged from about 15 to 45 mS/m: and that of the more highly contaminated zones in sand and gravel ranged from about 10 to more than 80 mS/m. Specific conductance of water samples from screened intervals in sand and gravel at selected monitoring well installations was significantly correlated with KM conductivity.
CM logging can be used in glacial sand-and-gravel aquifer investigations to (1) determine optimum depths for the placement of monitoring well screens: (2) provide a nearly continuous vertical profile of specific conductance to complement depth-specific water quality samples; and (3) identify temporal changes in water quality through sequential logging. Detailed lithologic or gamma logs, preferably both, need to be collected along with the F.M logs to define zones in which elevated EM conductivity is caused by the presence of sill and clay beds rather than contamination. 相似文献
The major hydrogeologic factors that affected KM log response at the five sites were the dissolved solids concentration of the ground water and the silt and clay content in the aquifer. KM conductivity of sand and gravel with uncontaminated water ranged from less than 5 to about 10 millisiemens per meter (mS/m); that of silt and clay zones ranged from about 15 to 45 mS/m: and that of the more highly contaminated zones in sand and gravel ranged from about 10 to more than 80 mS/m. Specific conductance of water samples from screened intervals in sand and gravel at selected monitoring well installations was significantly correlated with KM conductivity.
CM logging can be used in glacial sand-and-gravel aquifer investigations to (1) determine optimum depths for the placement of monitoring well screens: (2) provide a nearly continuous vertical profile of specific conductance to complement depth-specific water quality samples; and (3) identify temporal changes in water quality through sequential logging. Detailed lithologic or gamma logs, preferably both, need to be collected along with the F.M logs to define zones in which elevated EM conductivity is caused by the presence of sill and clay beds rather than contamination. 相似文献
18.
A new computer program, FLASH (Flow-Log Analysis of Single Holes), is presented for the analysis of borehole vertical flow logs. The code is based on an analytical solution for steady-state multilayer radial flow to a borehole. The code includes options for (1) discrete fractures and (2) multilayer aquifers. Given vertical flow profiles collected under both ambient and stressed (pumping or injection) conditions, the user can estimate fracture (or layer) transmissivities and far-field hydraulic heads. FLASH is coded in Microsoft Excel(5) with Visual Basic for Applications routines. The code supports manual and automated model calibration. 相似文献
19.
Understanding the Geometry of Connected Fracture Flow with Multiperiod Oscillatory Hydraulic Tests 下载免费PDF全文
下载免费PDF全文 An understanding of the spatial and hydraulic properties of fast preferential flow pathways in the subsurface is necessary in applications ranging from contaminant fate and transport modeling to design of energy extraction systems. One method for the characterization of fracture properties over interwellbore scales is Multiperiod Oscillatory Hydraulic (MOH) testing, in which the aquifer response to oscillatory pressure stimulations is observed. MOH tests were conducted on isolated intervals of wells in siliciclastic and carbonate aquifers in southern Wisconsin. The goal was to characterize the spatial properties of discrete fractures over interwellbore scales. MOH tests were conducted on two discrete fractured intervals intersecting two boreholes at one field site, and a nest of three piezometers at another field site. Fracture diffusivity estimates were obtained using analytical solutions that relate diffusivity to observed phase lag and amplitude decay. In addition, MOH tests were used to investigate the spatial extent of flow using different conceptual models of fracture geometry. Results indicated that fracture geometry at both field sites can be approximated by permeable two‐dimensional fracture planes, oriented near‐horizontally at one site, and near‐vertically at the other. The technique used on MOH field data to characterize fracture geometry shows promise in revealing fracture network characteristics important to groundwater flow and transport. 相似文献
20.
《Advances in water resources》1999,22(6):645-656
Observations of periodic components of measured heads have long been used to estimate aquifer diffusivities. The estimations are often made using well-known solutions of linear differential equations for the propagation of sinusoidal boundary fluctuations through homogeneous one-dimensional aquifers. Recent field data has indicated several instances where the homogeneous aquifer solutions give inconsistent estimates of aquifer diffusivity from measurements of tidal lag and attenuation. This paper presents new algebraic solutions for tidal propagation in spatially heterogeneous one-dimensional aquifers. By building on existing solutions for homogeneous aquifers, comprehensive solutions are presented for composite aquifers comprising of arbitrary (finite) numbers of contiguous homogeneous sub-aquifers and subject to sinusoidal linear boundary conditions. Both Cartesian and radial coordinate systems are considered. Properties of the solutions, including rapid phase shifting and attenuation effects, are discussed and their practical relevance noted. Consequent modal dispersive effects on tidal waveforms are also examined via tidal constituent analysis. It is demonstrated that, for multi-constituent tidal forcings, measured peak heights of head oscillations can seem to increase, and phase lags seem to decrease, with distance from the forcing boundary unless constituents are separated and considered in isolation. 相似文献